The fact that this exterior domain can touch arbitrarily many interior subdomains and that the diameter of its boundary is larger than those of the interior subdomains leads to special difficulties in the analysis. PhD thesis as PDF file 2. First, we consider the case of unbounded domains, where one subdomain corresponds to an exterior problem, while the other subdomains are bounded. Ulrich Langer External Referee: We also demonstrate that FETI preconditioners can lead to robust behavior even for certain coefficient distributions that are highly varying in the vicinity of the subdomain interfaces. Toward an assessment of generalized opinion leadership:

Furthermore, the bound is independent of jumps in the diffusion coefficient across subdomain interfaces. Considering benchmark problems involving highly singular eigensolutions, we demonstrate the performance of the constructed preconditioners and the eigenvalue solver in combination with hp -discretization on geometrically refined, anisotropic meshes. The key point is to respect the de Rham Complex already in the construction of the finite element basis functions and not, as usual, only for the definition of the local FE-space. For a listing of open PhD positions, see the latest news. The main contribution of this work is a general, unified construction principle for H curl – and H div -conforming finite elements of variable and arbitrary order for various element topologies suitable for unstructured hybrid meshes. This requires the solution of a potential problem, which can be done approximately by a couple of PCG-iterations.

Furthermore, the bound is independent of jumps in the diffusion coefficient across subdomain interfaces. In the next step we extend the gradient functions to a hierarchical and conforming basis of the desired polynomial space.

The hp -version of FEM combines local mesh refinement h and local increase of the polynomial order of the approximation space p. Numerical linx illustrate the robustness and performance of the method.

PhD thesis as PDF file 1. Considering benchmark problems involving highly singular eigensolutions, we demonstrate the performance of the constructed preconditioners and the eigenvalue solver in combination with hp -discretization on geometrically refined, anisotropic meshes. Our results are confirmed in numerical experiments.

# NUMA: Finished PhD Theses – Dipl.-Ing. Clemens Pechstein

A main advantage is that we can choose an arbitrary polynomial order on each edge, face, and cell without destroying the global exact sequence. Current dissertations Author Working title Mag. Axel Klawonn University of Duisburg-Essen, Germany Finite and boundary element discretizations of elliptic partial differential equations result in large linear systems of algebraic equations.

Ulrich Langer External Referee: The exterior problem is approximated using the boundary element method. Behaviour, Risk Taking and Personality Asc.

# NUMA – PhD Theses – Sabine Zaglmayr

By our separate treatment of edge-based, face-based, and cell-based functions, and by including the corresponding gradient functions, we can establish the local exact sequence property: A challenging topic in computational electromagnetics is the Maxwell eigenvalue problem.

Klaus Priller The role of interpersonal influence among the elderly in dealing with information and communication technologies Dipl. We prove rigorous libz for the condition number of the preconditioned FETI system that depend only on the coefficient variation in the vicinity of the subdomain interfaces.

A short outline of the construction is as follows. Furthermore, the incorporation of a coarse solve ensures the scalability of the method, which means that the number of iterations is independent of the number of subdomains.

Second, we consider elliptic equations with highly heterogeneous coefficient distributions. The key point is to respect the de Rham Complex already in the construction of the finite element basis functions and not, hku usual, only for the definition of the local FE-space.

To be more precise, if the coefficient varies only moderately in a layer near the boundary of each subdomain, the method is proved to be robust with respect to arbitrary variation in the interior of each subdomain and with respect to coefficient jumps across subdomain interfaces.

## Johannes Kepler University Linz (Linz/Austria) – JKU goes Gender – prize for dissertation

The fact that this exterior domain can touch arbitrarily many interior subdomains and that the diameter of its boundary is larger than those of the interior subdomains leads to special difficulties in the analysis. We also demonstrate that FETI preconditioners can lead to robust behavior even for certain coefficient distributions that are highly varying in the vicinity of the subdomain interfaces.

The main difficulty in the construction of efficient and parameter-robust preconditioners for electromagnetic problems is indicated by the different scaling of solenoidal and irrotational fields in the curl-curl problem.

The disseryation solution is then constructed iteratively from the repeated solution of local problems. Bernad Batinic including an explanation of the topic of interest dissretation well as a short CV including a list of any publications and conference contributions. In particular, the condition number of the corresponding preconditioned system is bounded in terms of a logarithmic expression in the local problem size. For a listing of open PhD positions, see the latest news.

For details, please refer to the curriculum jki the given doctoral program as the online course cataloge KUSSS. Due to the local exact sequence property this is already satisfied for simple splitting strategies. PhD thesis as PDF file 2. Robust Schwarz-type methods for Maxwell’s equations rely on a Dissfrtation splitting, which also has to provide a correct splitting of the kernel of liinz curl-operator.

Since the desired eigenfunctions belong to the orthogonal complement of the gradient functions, we have to perform an orthogonal projection in each iteration step. Timo Gnambs Toward an assessment of generalized opinion leadership: Leszek DemkowiczUniversity of Texas at Austin.